{"paper":{"title":"Counting 4-Patterns in Permutations Is Equivalent to Counting 4-Cycles in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Bart{\\l}omiej Dudek, Pawe{\\l} Gawrychowski","submitted_at":"2020-10-01T12:25:52Z","abstract_excerpt":"Permutation $\\sigma$ appears in permutation $\\pi$ if there exists a subsequence of $\\pi$ that is order-isomorphic to $\\sigma$. The natural question is to check if $\\sigma$ appears in $\\pi$, and if so count the number of occurrences. We know that for any fixed length~k, we can check if a given pattern of length k appears in a permutation of length n in time linear in n, but being able to count all such occurrences in $f(k)\\cdot n^{o(k/\\log k)}$ time would refute the exponential time hypothesis (ETH). This motivates a systematic study of the complexity of counting occurrences for different patte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.00348","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.00348/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}